Add unit test for order=3
The unit test uses the policy rules of Fernandez-Villaverde et al. (2011)'s "Risk matter" derived from Mathematica to compare them to the Dynare matrices. If the policy functions differ by more than 1e-9, an error is produced.time-shift
Johannes Pfeifer
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/*
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* This file replicates the IRFs of the small open economy model described in
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* Jesús Fernández-Villaverde, Pablo Guerrón-Quintana,
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* Juan F. Rubio-Ramírez, and Martin Uribe (2011): "Risk Matters",
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* American Economic Review 101 (October 2011): 2530–2561.
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*
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* This implementation was written by Benjamin Born and Johannes Pfeifer. Please
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* note that the following copyright notice only applies to this Dynare
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* implementation of the
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* model.
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*/
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/*
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* Copyright (C) 2013 Dynare Team
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*
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* This file is part of Dynare.
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*
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* Dynare is free software: you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation, either version 3 of the License, or
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* (at your option) any later version.
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*
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* Dynare is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with Dynare. If not, see <http://www.gnu.org/licenses/>.
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*/
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var sigma_r sigma_tb eps_r eps_tb X D K lambda C H Y I phi r;
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varexo u_sigma_r u_sigma_tb u_r u_tb u_x ;
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predetermined_variables K D;
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parameters r_bar rho_eps_r sigma_r_bar rho_sigma_r eta_r
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rho_eps_tb sigma_tb_bar rho_sigma_tb eta_tb
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delta alppha nu rho_x betta
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Phi phipar sigma_x D_bar omega eta;
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// Calibration from Table 3
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rho_eps_r=0.97;
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sigma_r_bar=-5.71;
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rho_sigma_r=0.94;
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eta_r=0.46;
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// Calibration from Table 4
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rho_eps_tb=0.95;
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sigma_tb_bar=-8.06; %8.05 in paper, but 8.06 in code
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rho_sigma_tb=0.94;
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eta_tb=0.13;
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nu=5; %inverse of the elasticity of intertemporal substitution
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eta=1000; %elasticity of labor to wages
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delta=0.014; %depreciation
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alppha = 0.32; % capital income share
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rho_x=0.95; %autocorrelation TFP
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// Calibration from Table 6 //
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r_bar=log(0.02);
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betta = 1/(1+exp(r_bar)); %discount factor
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Phi=0.001; %debt elasticity
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D_bar= 4; % steady state debt
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phipar=95; % capital adjustment costs
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sigma_x=log(0.015);
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omega=1;
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model;
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(exp(C))^-nu=exp(lambda);
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exp(lambda)/(1+exp(r))=exp(lambda)*Phi*((D(+1))-D_bar)+betta*exp(lambda(+1));
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-exp(phi)+betta*((1-delta)*exp(phi(+1))+alppha*exp(Y(+1))/exp(K(+1))*exp(lambda(+1)))=0;
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omega*exp(H)^eta=(1-alppha)*exp(Y)/exp(H)*exp(lambda);
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exp(phi)*(1-phipar/2*((exp(I)-exp(I(-1)))/exp(I(-1)))^2-phipar*exp(I)/exp(I(-1))*((exp(I)-exp(I(-1)))/exp(I(-1))))+betta*exp(phi(+1))*phipar*(exp(I(+1))/exp(I))^2*((exp(I(+1))-exp(I))/exp(I))=exp(lambda);
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exp(Y)=exp(K)^alppha*(exp(X)*exp(H))^(1-alppha);
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X=rho_x*X(-1)+exp(sigma_x)*u_x;
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exp(K(+1))=(1-delta)*exp(K)+(1-phipar/2*(exp(I)/exp(I(-1))-1)^2)*exp(I);
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exp(Y)-exp(C)-exp(I)=(D)-(D(+1))/(1+exp(r))+Phi/2*((D(+1))-D_bar)^2;
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exp(r)=exp(r_bar)+eps_tb+eps_r;
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eps_tb=rho_eps_tb*eps_tb(-1)+exp(sigma_tb)*u_tb;
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sigma_tb=(1-rho_sigma_tb)*sigma_tb_bar+rho_sigma_tb*sigma_tb(-1)+eta_tb*u_sigma_tb;
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eps_r=rho_eps_r*eps_r(-1)+exp(sigma_r)*u_r;
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sigma_r=(1-rho_sigma_r)*sigma_r_bar+rho_sigma_r*sigma_r(-1)+eta_r*u_sigma_r;
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end;
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initval;
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sigma_tb=sigma_tb_bar;
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sigma_r=sigma_r_bar;
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eps_r=0;
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eps_tb=0;
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D=D_bar;
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% steady states taken from Mathematica code
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C=0.8779486025329908;
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K=3.293280327636415;
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lambda=-4.389743012664954;
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H=-0.0037203652717462993;
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phi=-4.389743012664954;
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I=-0.9754176217303792;
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Y=1.0513198564588924;
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r=r_bar;
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end;
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shocks;
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var u_x; stderr 1;
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var u_r; stderr 1;
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var u_tb; stderr 1;
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var u_sigma_tb; stderr 1;
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var u_sigma_r; stderr 1;
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end;
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resid(1);
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options_.solve_tolf=1E-12;
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steady(solve_algo=3);
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check;
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stoch_simul(order=3,pruning,irf=0,nocorr,nofunctions,nomoments) C I Y H r D K lambda phi;
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comparison_policy_functions_dynare_mathematica;
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@ -0,0 +1,125 @@
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%read in the FV et al. policy functions derived from Mathematica
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load policyfunctions
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order=options_.order;
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dr=oo_.dr;
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nx =size(dr.ghx,2);
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nu =size(dr.ghu,2);
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k = find(dr.kstate(:,2) <= M_.maximum_lag+1);
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klag = dr.kstate(k,[1 2]);
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state_vars=dr.order_var(klag(:,1));
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%order of endogenous variables in FV et al. paper: c, invest, y, h, r, dp, kp, lambda, pi
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varlist_FV={'C';'I';'Y';'H';'r';'D';'K';'lambda';'phi'};
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for ii=1: length(varlist_FV)
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FV_endo_order(ii,1)=strmatch(varlist_FV(ii),M_.endo_names(dr.order_var,:),'exact');
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end
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% order in states of FV et al. paper:
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% exogenous: usigmar usigmatb ur utb ug
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varlist_FV_exo_states={'u_sigma_r';'u_sigma_tb';'u_r';'u_tb';'u_x'};
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for ii=1: length(varlist_FV_exo_states)
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FV_exo_order(ii)=strmatch(varlist_FV_exo_states(ii),M_.exo_names,'exact');
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end
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%followed by endogenous: sigmarlag sigmatblag erlag etblag glag investlag debt capital Lambda
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varlist_FV_endo_states={'sigma_r';'sigma_tb';'eps_r';'eps_tb';'X';'I';'D';'K'};
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for ii=1: length(varlist_FV_endo_states)
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FV_endo_state_order(ii)=strmatch(varlist_FV_endo_states(ii),M_.endo_names(state_vars,:),'exact');
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end
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%% First order
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gx_dyn(:,1:nu)=dr.ghu(FV_endo_order,FV_exo_order);
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gx_dyn(:,nu+1:nu+nx)=dr.ghx(FV_endo_order,FV_endo_state_order);
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if max(max(abs(gx(:,1:end-1)-gx_dyn))) > 1e-9
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max(max(abs(gx(:,1:end-1)-gx_dyn)))
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error('First order wrong')
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else max(max(abs(gx(:,1:end-1)-gx_dyn)));
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end
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%% Second order
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gxx_dyn=zeros(size(gxx));
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for endo_iter_1=1:nx
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for endo_iter_2=1:nx
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gxx_dyn(nu+endo_iter_1,nu+endo_iter_2,:)=dr.ghxx(FV_endo_order,(FV_endo_state_order(endo_iter_1)-1)*nx+FV_endo_state_order(endo_iter_2));
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end
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end
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for exo_iter_1=1:nu
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for exo_iter_2=1:nu
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gxx_dyn(exo_iter_1,exo_iter_2,:)=dr.ghuu(FV_endo_order,(FV_exo_order(exo_iter_1)-1)*nu+FV_exo_order(exo_iter_2));
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end
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end
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for endo_iter_1=1:nx
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for exo_iter_1=1:nu
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gxx_dyn(nu+endo_iter_1,exo_iter_1,:)=dr.ghxu(FV_endo_order,(FV_endo_state_order(endo_iter_1)-1)*nu+FV_exo_order(exo_iter_1));
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gxx_dyn(exo_iter_1,nu+endo_iter_1,:)=dr.ghxu(FV_endo_order,(FV_endo_state_order(endo_iter_1)-1)*nu+FV_exo_order(exo_iter_1));
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end
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end
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% deal with Lambda, the perturbation parameter
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for ii=1:length(FV_endo_order)
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gxx_dyn(14,14,:)=dr.ghs2(FV_endo_order);
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end
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if max(max(max(abs(gxx-gxx_dyn)))) > 1e-9
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max(max(max(abs(gxx-gxx_dyn))))
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error('Second order wrong')
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else max(max(max(abs(gxx-gxx_dyn))));
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end
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%% third order
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gxxx_dyn=zeros(size(gxxx));
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for endo_iter_1=1:nx
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for endo_iter_2=1:nx
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for endo_iter_3=1:nx
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gxxx_dyn(nu+endo_iter_1,nu+endo_iter_2,nu+endo_iter_3,:)=dr.ghxxx(FV_endo_order,(FV_endo_state_order(endo_iter_1)-1)*nx*nx+(FV_endo_state_order(endo_iter_2)-1)*nx+FV_endo_state_order(endo_iter_3));
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end
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end
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end
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for exo_iter_1=1:nu
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for exo_iter_2=1:nu
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for exo_iter_3=1:nu
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gxxx_dyn(exo_iter_1,exo_iter_2,exo_iter_3,:)=dr.ghuuu(FV_endo_order,(FV_exo_order(exo_iter_1)-1)*nu*nu+(FV_exo_order(exo_iter_2)-1)*nu+FV_exo_order(exo_iter_3));
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end
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end
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end
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for endo_iter_1=1:nx
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for endo_iter_2=1:nx
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for exo_iter=1:nu
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gxxx_dyn(nu+endo_iter_1,nu+endo_iter_2,exo_iter,:)=dr.ghxxu(FV_endo_order,(FV_endo_state_order(endo_iter_1)-1)*nx*nu+(FV_endo_state_order(endo_iter_2)-1)*nu+FV_exo_order(exo_iter));
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gxxx_dyn(exo_iter,nu+endo_iter_2,nu+endo_iter_1,:)=dr.ghxxu(FV_endo_order,(FV_endo_state_order(endo_iter_1)-1)*nx*nu+(FV_endo_state_order(endo_iter_2)-1)*nu+FV_exo_order(exo_iter));
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gxxx_dyn(nu+endo_iter_1,exo_iter,nu+endo_iter_2,:)=dr.ghxxu(FV_endo_order,(FV_endo_state_order(endo_iter_1)-1)*nx*nu+(FV_endo_state_order(endo_iter_2)-1)*nu+FV_exo_order(exo_iter));
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end
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end
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end
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for endo_iter_1=1:nx
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for exo_iter_1=1:nu
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for exo_iter_2=1:nu
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gxxx_dyn(nu+endo_iter_1,exo_iter_1,exo_iter_2,:)=dr.ghxuu(FV_endo_order,(FV_endo_state_order(endo_iter_1)-1)*nu*nu+(FV_exo_order(exo_iter_1)-1)*nu+FV_exo_order(exo_iter_2));
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gxxx_dyn(exo_iter_1,nu+endo_iter_1,exo_iter_2,:)=dr.ghxuu(FV_endo_order,(FV_endo_state_order(endo_iter_1)-1)*nu*nu+(FV_exo_order(exo_iter_1)-1)*nu+FV_exo_order(exo_iter_2));
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gxxx_dyn(exo_iter_1,exo_iter_2,nu+endo_iter_1,:)=dr.ghxuu(FV_endo_order,(FV_endo_state_order(endo_iter_1)-1)*nu*nu+(FV_exo_order(exo_iter_1)-1)*nu+FV_exo_order(exo_iter_2));
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end
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end
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end
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% deal with Lambda, the perturbation parameter
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gxxx_dyn(14,14,1:5,:)=oo_.dr.ghuss(FV_endo_order,FV_exo_order)';
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gxxx_dyn(14,1:5,14,:)=oo_.dr.ghuss(FV_endo_order,FV_exo_order)';
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gxxx_dyn(1:5,14,14,:)=oo_.dr.ghuss(FV_endo_order,FV_exo_order)';
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gxxx_dyn(14,14,nu+1:13,:)=oo_.dr.ghxss(FV_endo_order,FV_endo_state_order)';
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gxxx_dyn(14,14,14,:)=0;
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gxxx_dyn(14,nu+1:13,14,:)=oo_.dr.ghxss(FV_endo_order,FV_endo_state_order)';
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gxxx_dyn(nu+1:13,14,14,:)=oo_.dr.ghxss(FV_endo_order,FV_endo_state_order)';
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if max(max(max(max(abs(gxxx-gxxx_dyn))))) > 1e-9
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max(max(max(max(abs(gxxx-gxxx_dyn)))))
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error('Third order wrong')
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else max(max(max(max(abs(gxxx-gxxx_dyn)))))
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end
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